Download Levitated droplet dye laser

Levitated droplet dye laser
H. Azzouz,1 L. Alkhafadiji,2 S. Balslev,1
J. Johansson,3 N. A. Mortensen,1 S. Nilsson,2 and A. Kristensen1
1 MIC – Department of Micro and Nanotechnology, Nano•DTU,
Technical University of Denmark, Building 345east, DK-2800 Kongens Lyngby, Denmark
2 Pure and Applied Biochemistry, Center for Chemistry and Chemical Engineering,
Lund University, P.O. Box 124, 221 00 Lund, Sweden
3 AstraZeneca, R&D Mölndal, Analytical Development, Mölndal, Sweden
[email protected]
Abstract: We present the first observation, to our knowledge, of lasing
from a levitated, dye droplet. The levitated droplets are created by computer controlled pico-liter dispensing into one of the nodes of a standing
ultrasonic wave (100 kHz), where the droplet is trapped. The free hanging
droplet forms a high quality optical resonator. Our 750 nL lasing droplets
consist of Rhodamine 6G dissolved in ethylene glycol, at a concentration of
0.02 M. The droplets are optically pumped at 532 nm light from a pulsed,
frequency doubled Nd:YAG laser, and the dye laser emission is analyzed by
a fixed grating spectrometer. With this setup we have achieved reproducible
lasing spectra in the visible wavelength range from 610 nm to 650 nm. The
levitated droplet technique has previously successfully been applied for a
variety of bio-analytical applications at single cell level. In combination
with the lasing droplets, the capability of this high precision setup has
potential applications within highly sensitive intra-cavity absorbance
detection.
© 2006 Optical Society of America
OCIS codes: (140.2050) Dye lasers; (140.4780) Optical resonators; (140.7300) Visible lasers;
(999.9999) Ultrasonic levitation
References and links
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47 (1997).
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237 (1996).
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coupled to Raman spectroscopy,” Anal. Chem. 75, 2177 – 2180 (2003).
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prospects,” Phys. Chem. Chem. Phys. 6, 474 – 487 (2004).
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nucleation conditions using levitated drops for protein crystallization,” Anal. Chem. 75, 1733 – 1740 (2003).
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Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4374
12. Tech5 AG, URL http://www.tec5.com.
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microlitres and submicrolitres,” Pharm. Ind. 59, 814 – 817 (1997).
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Heinemann, Oxford, 1987).
15. A. L. Yarin, D. A. Weiss, G. Brenn, and D. Rensink, “Acoustically levitated drops: drop oscillation and break-up
driven by ultrasound modulation,” Int. J. Multiph. Flow 28, 887–910 (2002).
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Phys. Rev. A 67, 033,806 (2003).
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Lett. 21, 453 – 455 (1996).
1. Introduction
Optical micro cavities in general are receiving considerable interest due to their size and geometry dependent resonant frequency spectrum and the variety of applications [1]. Micro-droplets
constitute an interesting medium for micro-cavity optics in terms of e.g. lasing emission properties [2] and manifestation of chaotic wave dynamics [3, 4]. Combined with ultrasonic levitation
techniques [5] micro-droplets may also provide an interesting environment for analytical chemistry [6] including intra-cavity surface-enhanced Raman spectroscopy [7, 8].
Lasing in freely falling droplets was first reported by Qian et al. [2] which stimulated a
significant interest in the optical properties of droplets, see e.g. Datsyuk [9] and references
therein. Parallel to this there has been a significant attention to ultrasonic levitation [5] from
the chemical community [6] allowing for studies of e.g. protein crystallization [10]. Combining ultrasonic levitation with the optical properties of droplets holds great promise for highly
sensitive intra-cavity absorbance detection system with prospects for single-molecule detection [8]. However, such applications rely heavily on both reproducible loading of droplets and
subsequent reproducible generation of laser emission spectra by external pumping.
In this paper we present the first observation, to our knowledge, of reproducible lasing
from levitated 750 nl dye droplets. Droplets are optically pumped at 532 nm by a pulsed,
frequency doubled Nd:YAG laser and emission is analyzed by fixed grating spectrometry.
The levitated droplet constitutes a highly sensitive intra-cavity absorbance detection system
with prospects for single-molecule detection [8] and the possibility for computer-generated ondemand droplets holds great promise for applications in high-throughput chemical analysis.
a
b
c
d
Fig. 1. a) Photograph of a lasing levitated micro-droplet. b) Schematics of ultrasonic
field with the micro-droplet being trapped at a node in the ultrasonic field. c) Schematics of whispering-gallery modes in a (2D) spherical cavity. d) Numerical example of a
whispering-gallery mode in a (2D) spherical cavity.
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Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4375
Fig. 2. Reproducible lasing spectra from dye doped micro-droplets. Each spectrum is obtained in a fixed setup by a well-controlled loading of an EG droplet with a Rh6G dye
which is subsequently pumped above threshold, see Fig. 3(b). The spectra are averaged
over three pump pulses.
2. Experimental setup and results
Ultrasonic levitation is a technique that facilitates the performance of a variety of investigations
on small volumes of samples, i.e. liquid droplets and particles. It suspends the object levitated
in the nodal point of an ultrasonic standing wave, see Fig. 1(b). The technique was introduced
in the 1930’s and does not rely on any specific properties of the sample except size and mass.
The method has been used extensively in bio-analytical and analytical chemistry applications,
see e.g. [6, 11] and references therein.
The ultrasonic levitator [12] consists of an ultrasonic transducer and a solid reflector supporting standing waves, see Fig. 1(a) and (b). In this work the levitator is operated at a frequency
of Ωvib /2π ∼ 100 kHz corresponding to a wavelength of Λ ∼ 6 mm. The levitator can hold
particles of radius a < Λ and droplets with a ∼ Λ/6 require a minimum of ultrasonic power.
Large droplets may be deformed by the body forces (gravity and ultrasonic pressure gradients),
which in practice limits the droplet size to a < ξ where the capillary length ξ is in the millimeter range for a water droplet. Furthermore, the droplet shape may also be spherically deformed
by applying a large ultrasonic pressure amplitude.
In our experiments we used Rhodamine 6G (Rh6G) laser dye dissolved in ethyleneglycole (EG). The liquid sample was placed in a nodal point of the levitator by means of
a computer controlled piezo-electric micro dispenser [13]. A droplet with a total volume of
V = (4π /3)a3 ∼ 750 nl was formed by repeated addition of pL drops.
The levitated dye droplet was optically pumped by a pulsed, frequency-doubled Nd:YAG
laser (λ = 532 nm) with a pulse length of 5 ns and a repetition rate of 10 Hz. The light emitted
from the micro-droplet was collected by an optical fiber placed at an angle of approximately
50 degrees relative to the pump laser beam. The emission was analyzed in a fixed-grating spectrometer with a resolution of 0.15 nm.
Evaporation and dye bleaching could hinder the applicability of the dye droplet as a lasing
device. In order to minimize these effects, we used a measurement scheme, where nominally
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Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4376
identical droplets are loaded consecutively, and each droplet is only pumped with 100 pulses
(corresponding to a duration of 10 s) from the Nd:YAG laser, before it is replaced by the next
droplet. We have not systematically investigated the performance of the dye droplet lasers for
more than 100 pulses.
In Fig. 2 we show 5 emission spectra obtained from normally identical V = 750 nl EG
droplets, with a Rh6G concentration of 2 × 10 −2 mol/L. The laser was pumped above the
threshold. The observed variations in output power are attributed to fluctuations in the pump
power.
In a second measurement series we demonstrate the lasing action of the dye droplet where
consecutively loaded droplets are pumped at different average pump power. In Fig. 3(a) we
a
b
Fig. 3. a) Cavity output power for increasing and decreasing average pump power. Each
spectrum is obtained in a fixed setup by pumping an EG droplet with a Rh6G dye. The pump
power is first increased from zero up to level around 1000 mW (dashed curves) and subsequently again lowered (solid curves). The spectra are averaged over three pump pulses.
b) Cavity output power versus mean pump power. The dashed lines are guides to the eyes
indicating a lasing threshold of around 500 mW in the mean pump power.
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Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4377
show the measured spectra and in Fig. 3(b) we show the dye droplet output power versus pump
power. In the measurement sequence the pump power was first increased from 150 mW to
900 mW and subsequently decreased again. The reproducibility of the obtained spectra and the
lasing threshold is seen from panels a and b, respectively.
3. Discussion
In the following we briefly address the optical and mechanical modes, to assess the influence
on the optical performance of levitated droplet dye lasers and their applications for intra-cavity
sensing.
3.1. Optical modes
For a spherical resonator the whispering-gallery modes (WGMs) are characterized by their
radial quantum number p as well as by their angular momentum quantum number and the
azimuthal quantum number m which can have (2 + 1) values, i.e. ω p has a (2 + 1) degeneracy [8]. For the lowest-order radial modes (p = 1), see Fig. 1(d), the resonances are to a good
approximation given by nχ ∼ where χ = ka is the so-called dimensionless size parameter,
n is the refractive index, a is the radius of the droplet, and k = ω /c = 2π /λ is the free-space
wave vector. The modes are thus equally spaced in frequency and the corresponding spacing in
wavelength is [8]
2
−1 2
1/2
∂λ Δχ λ tan (n − 1) ,
(1)
Δλ = ∂χ 2π a (n2 − 1)1/2
where the last fraction indeed has a 1/n asymptotic dependence for a large refractive index,
n 1. For the EG droplets in the experiments the corresponding mode spacing is of the order
Δλ ∼ 0.1 nm which is not resolved in our present experiments. However, V = 100 pL droplets
(a ∼ 30 μ m) have been achieved in different experiments by operating the levitator at 100 kHz.
This would increase the mode spacing to Δλ ∼ 1 nm.
3.2. Droplet shape and mechanical modes
The shape of the droplet may be understood from Gibbs
free-energy arguments where one naturally defines the characteristic capillary length ξ = γ /ρ g with γ being the surface tension,
ρ is the liquid mass density, and g is magnitude of the gravitational field [14]. A droplet with
a characteristic size a ξ will have a shape strongly determined by the surface tension and a
spherical shape will then obviously minimize the Gibbs free energy. For a free water droplet
in air ξ ∼ 2.7 mm. In our experiments, where a ∼ 500 μ m, the spherical shape is not perturbed
significantly by body forces.
We emphasize that in principle the levitated droplet is a complicated dynamical system, see
e.g. [15]. However, as analyzed already by Rayleigh in 1879 [14] the vibrational spectrum of a
liquid droplet originates from two classes of modes; surface-tension driven surface modes and
compression-driven compressional modes. Since the liquid can be considered incompressible
the latter class of modes is in the high-frequency regime while the low-frequency response is
due to surface-shape oscillations conserving the volume. The surface vibrational modes are similar to the optical WGMs and are characterized by their angular momentum quantum number
vib . For low amplitude oscillations Rayleigh found that [14]
γ vib (vib − 1)(vib + 2)
ωvib =
, vib = 2, 3, 4, . . .
(2)
ρ a3
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Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4378
A droplet of a given radius acan thus not be vibrationally excited by the ultrasonic pressure
field at frequencies Ω vib < 8γ /ρ a3. For a driving frequency of 100 kHz this implies that
water droplets of radius below 10 μ m are not vibrationally excited.
3.3. Prospects for intra-cavity sensing
The prospects for intra-cavity sensing in liquid dye droplets correlate strongly with the optical
cavity Q factor. The WGMs each have a resonant frequency ω with a width δ ω = 1/τ where τ
is the lifetime of a photon in the mode. The corresponding quality factor Q = ω /δ ω of WGMs
is determined by several factors including intrinsic radiative losses originating from the finite
curvature of the droplet surface Q rad , absorption due to the cavity medium Q abs , and broadening
of resonances due to vibrational interaction with the ultrasonic field Q vib , i.e.
−1
−1
Q−1 = Q−1
rad + Qabs + Qvib .
(3)
For the radiative loss Q rad increases close to exponentially with the size parameter χ and for
a refractive index n ∼ 1.45 we have Q rad ∼ 105 and Qrad ∼ 1012 for χ equal to 50 and 100,
respectively [16]. In the case of bulk absorption we have [17]
Qabs =
2π n
χ
=
αλ
αa
(4)
where α is the absorption coefficient of the cavity medium.
The broadening of the WGMs by interaction with the vibrational modes is complicated, but
we may immediately disregard the high-frequency compressional modes leaving only the lowfrequency surface-tension driven modes for concern. Even though the realistically attainable
droplet (a > 40 μ m) will be vibrationally excited by the ultrasonic pressure field, the influence
of the disturbance could be suppressed by short pump pulse operation. Finally, static, deformations of the cavity may give rise to partial chaotic ray dynamics with a universal, frequency
independent, broadening of the WGM resonances which will decrease Q rad [3, 4]. A similar
vibration-induced decrease of Q rad is expected.
4. Conclusion
In conclusion we have demonstrated a reproducible laser action from an ultrasonically levitated laser dye droplet, when nominally identical 750 nL droplets are consecutively loaded and
optically pumped by a pulsed frequency-doubled Nd:YAG laser. The present droplets show reproducible multi-mode lasing. This system is considered a potential candidate for intra-cavity
sensing, and the limitations induced by ultrasonic field were discussed.
Acknowledgments
This work is supported by the Danish Technical Research Council (grant no. 26-02-0064) and
the Danish Council for Strategic Research through the Strategic Program for Young Researchers
(grant no. 2117-05-0037). Financial support from the Swedish Research Council (VR), Crafoordska Stiftelsen, Kungliga Fysiografiska Sällskapet i Lund, Centrala Försöksdjursnämnden,
and the R. W. Johnson Research Institute is gratefully acknowledged.
#69304 - $15.00 USD
(C) 2006 OSA
Received 23 March 2006; revised 24 April 2006; accepted 27 April 2006
15 May 2006 / Vol. 14, No. 10 / OPTICS EXPRESS 4379